Thermal and magnetoelastic properties of $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$ in the field-induced low-temperature states

Thermal and magnetoelastic properties of $α - {RuCl}_{3}$ in the field-induced low-temperature states

Rico Schönemann, Shusaku Imajo, Franziska Weickert, Jiaqiang Yan, David G. Mandrus, Yasumasa Takano, Eric L. Brosha, Priscila F. S. Rosa, Stephen E. Nagler, Koichi Kindo, and Marcelo Jaime

Phys. Rev. B 102, 214432 – Published 24 December 2020

Abstract

We discuss the implications that new magnetocaloric, thermal expansion, and magnetostriction data in $α − {RuCl}_{3}$ single crystals have on its temperature-field phase diagram and uncover the magnetic-field dependence of an apparent energy gap structure $Δ (H)$ that evolves when the low-temperature antiferromagnetic order is suppressed. We show that, depending on how the thermal expansion data are modeled, $Δ (H)$ can show a cubic field dependence and remain finite at zero field, consistent with the pure Kitaev model hosting itinerant Majorana fermions and localized $Z_{2}$ fluxes. Our magnetocaloric effect data provide, below $1 K$ , unambiguous evidence for dissipative phenomena at $H_{c}$ , a smoking gun for a first-order phase transition. Conversely, our results show little support for a phase transition from a QSL to a polarized paramagnetic state above $H_{c}$ .

Received 22 August 2020
Revised 4 December 2020
Accepted 8 December 2020

DOI:https://doi.org/10.1103/PhysRevB.102.214432

Physics Subject Headings (PhySH)

Antiferromagnetism Frustrated magnetism Magnetic phase transitions Magnetoelastic effect Magnetostriction Majorana fermions Phase diagrams Quantum phase transitions Thermal expansion

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Rico Schönemann ^1,*, Shusaku Imajo², Franziska Weickert ¹, Jiaqiang Yan^3,4, David G. Mandrus^3,4, Yasumasa Takano⁵, Eric L. Brosha⁶, Priscila F. S. Rosa⁷, Stephen E. Nagler⁸, Koichi Kindo², and Marcelo Jaime ^1,†

¹MPA-MAGLAB, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
²The Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
³Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37996, USA
⁴Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996, USA
⁵Department of Physics, University of Florida, Gainesville, Florida 32611, USA
⁶MPA-11, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
⁷MPA-CMMS, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
⁸Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

^*rschoenemann@lanl.gov
^†mjaime@lanl.gov; Present address: Physikalisch-Technische Bundesanstalt, Braunschweig 38116, Germany.

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Vol. 102, Iss. 21 — 1 December 2020

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Figure 1
Thermal expansion $Δ L / L_{0}$ as a function of temperature. The arrows indicate the onset of the antiferromagnetic ordering temperature $T_{N}$ at around $7 K$ (black arrow) as well as the broad feature present at $14 K$ (blue arrow). The inset shows the low-temperature magnetization of the same crystal recorded at a magnetic field of $100 Oe$ . A depiction of the fiber Bragg grating setup is shown in the bottom. The magnetic field is aligned along the optical fiber and parallel to the [1,1,0] crystallographic direction.
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Figure 2
(a) Thermal expansion $Δ L / L_{0}$ vs. temperature for different magnetic fields. Curves were shifted vertically for clarity. The gray shaded region indicates the antiferromagnetic transitions. (b) Thermal expansion coefficient $α$ for fields $H > 6 T$ . The solid red lines are fits representing a Schottky-like behavior according to equation (1) while the curve recorded at $6 T$ was fitted only for temperatures above $7 K$ , avoiding the antiferromagnetic transition. (c) Thermal expansion coefficient $α$ vs. temperature at zero magnetic field. (d) The gap $Δ (H)$ (squares), indicating a $H^{3}$ behavior (solid red line) and a finite gap $Δ_{0}$ at $μ_{0} H = 0 T$ . The triangles represents the activation energy extracted from fits using a single exponential function.
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Figure 3
(a) $Δ L / L$ vs. the magnetic field at $T = 1.6 K$ (black curve). The arrows denote the critical fields marking anomalies in the derivative $λ = (1 / L_{0}) \partial (Δ L / L) / \partial H$ (red line) between the different AFM phases ${zz}_{1}$ and ${zz}_{2}$ , as well as AFM and the partially field polarized paramagnetic state. The low field anomaly (blue arrow) is likely caused by magnetic domain flip as mentioned in the text. (b) Phase diagram of $α − {RuCl}_{3}$ extracted from magnetoelastic and MCE measurements. Open symbols represent the transition from the ${zz}_{1}$ to the ${zz}_{2}$ AFM state, and solid symbols indicate the transition between AFM order and the partially field polarized PM state.
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Figure 4
(a) Sample temperature vs. magnetic field under quasiadiabatic conditions. The shaded areas mark the first (blue) and second (gray) critical field, respectively. The arrows symbolize the field sweep direction. (b) Relative change of the sample temperature $Δ T / T$ as a function of the magnetic field under quasi-isothermal conditions, after a smooth background subtraction. (c) Expanded MCE curve at an initial temperature of $1.1 K$ . (d) Cartoon displaying the expected quasi-isothermal behavior of the MCE under reversible (second-order) and irreversible (first-order) conditions [38].
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Physical Review B

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Thermal and magnetoelastic properties of $α - {RuCl}_{3}$ in the field-induced low-temperature states

Rico Schönemann, Shusaku Imajo, Franziska Weickert, Jiaqiang Yan, David G. Mandrus, Yasumasa Takano, Eric L. Brosha, Priscila F. S. Rosa, Stephen E. Nagler, Koichi Kindo, and Marcelo Jaime

Phys. Rev. B 102, 214432 – Published 24 December 2020

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Physical Review B

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Thermal and magnetoelastic properties of α−RuCl3 in the field-induced low-temperature states

Rico Schönemann, Shusaku Imajo, Franziska Weickert, Jiaqiang Yan, David G. Mandrus, Yasumasa Takano, Eric L. Brosha, Priscila F. S. Rosa, Stephen E. Nagler, Koichi Kindo, and Marcelo Jaime

Phys. Rev. B 102, 214432 – Published 24 December 2020

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Thermal and magnetoelastic properties of $α - {RuCl}_{3}$ in the field-induced low-temperature states